Leo (centre) and Lucia (right) were found by their mother Marina Krim in their New York apartment (LiveJournal.com)

Two children were stabbed to death by their nanny in the bathtub of their luxury apartment near Central Park in New York yesterday.

Marina Krim, the mother of Lucia, six, and Leo, one, came home to find her children dead and their nanny, Yoselyn Ortega, with self-inflicted stab wounds.

Ortega, 50, was found in the bathroom with stab wounds to her neck and a kitchen knife close by, police said. She was taken to hospital and is in a critical condition, under police custody.

The children were pronounced dead at hospital. Their father was CNBC digital media executive Kevin Krim. He had been away on a business trip and was met by the police at the airport, following which was escorted to the hospital.

Rima Starr, a neighbour who lives on the same floor as the Krim family in the La Rochelle building, said she heard screams coming from the apartment at around 5.30pm.

"There was some kind of screaming about, 'You slit her throat!' It was horrible," she said.

Mrs Krim wrote on her blog how Leo Krim, one, was learning to speak on the day he was killed.

Starr also said she believes Ortega had been hired recently, adding that she had spoken with her the day before she murdered the children. "I met her in the elevator, the day before yesterday, and was making small talk."

Mrs Krim returned home with her three-year-old daughter, Nessie, after taking her to a swimming lesson.

She thought Lucia and Leo were out with Ortega. After finding out from the doorman of the building that they had not left, she discovered her children in the bathroom.

When the police arrived, Mrs Krim was screaming hysterically and hugging her surviving child.

Lucia Krim, six. Nanny Yoselyn Ortega stabbed Lucia and Leo to death in the bathroom of their home.

According to police, there was no water in the bath. Police commissioner Raymond Kelly said it is not clear how many times the children had been stabbed.

Jill Pace, 27, who lives nearby, told nydailynews.com: "It's awful. It makes me sick to my stomach. I can't even look at the building. You have to wonder what goes through someone's mind to do such a horrible thing."

Writing on her blog, Life with the Little Krim Kids, yesterday afternoon, Mrs Krim talked about how her youngest was learning to speak.

She wrote: "Leo speaks in the most adorable way possible. Firstly, he speaks super clearly, so you can understand every word is he is saying. And he does things like, '(I) want a fresh bagel' and 'Dito (what he calls himself) wants cold milk' and most adorable of all, 'No thank you' - he never uses 'No' alone, it's always paired with 'thank you'."

The police investigation is ongoing and no charges have been filed yet.

Mrs Krim was found clutching her surviving child, Nessie and screaming hysterically.